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Midterm05 - Department of Economics ECONOMETRICS I Fall...

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ECONOMETRICS I Fall 2005 – Tuesday, Thursday, 1:00 – 2:20 Professor William Greene Phone: 212.998.0876 Office: KMC 7-78 Home page:www.stern.nyu.edu/~wgreene Office Hours: Open Email: [email protected] URL for course web page: www.stern.nyu.edu/~wgreene/Econometrics/Econometrics.htm Midterm 1. In the classical regression model, y i = x i1 ′ β 1 + x i2 ′ β 2 + ε i , i = 1 ,…,n , E[ε i | X ] = 0, Var[ε i | X ]=σ 2 ; X 1 is K 1 variables and X 2 is K 2 variables. There are two possible estimators of β 1 , the first K 1 coefficients in the “long regression” of y on X 1 and X 2 and the K 1 coefficients in the short regression of y on X 1 . Let X = [ X 1 , X 2 ]. We will assume that plim[(1/n) X X ] = Q , a positive definite matrix. a. [5 points] Assume that plim[(1/n) X 1 X 2 ] ≠ 0 . Is either estimator unbiased? Is either estimator consistent? b. [5 points] Assume that plim[(1/n) X 1 X 2 ] = 0. Is either estimator unbiased? Is either estimator consistent? c. [5 points] Explain the difference between consistency and unbiasedness. Does either imply the other? Explain. d. [5 points] Suppose the assumption in a. is correct. The estimator we will use is the following: We will compute the long regression. F is the conventional F statistic for testing the null hypothesis that β 2 is zero. If F > 2, we will use the long estimator. If F < 2, we will use the short estimator. Is the estimator consistent? Unbiased? (Hint, you can think this one through to an answer without deriving a probability limit.) 2. The regressions for this problem are based on a sample of 27,326 observations, a survey of health care system usage taken in Germany over 7 years in the 1990s. The four regressions below are income equations based on the model Income = β 1 + β 2 Educ + β 3 Educ 2 + β 4 Married + β 5 Female + β 6 Hhkids + ε Department of Economics
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Educ is measured by years of schooling. Married and Hhkids are dummy variables for marital status and whether there are kids in the household, and Female = 1 for women, 0 for men. In the first regression, the dummy variable FEMALE is included; in the second, it is omitted.
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